Recently it has been proven that highly engineered grinding/polishing tools can be manufactured with controlled shapes and distributions of abrasives. This research is directed to understand the influence of the shapes of the micro-cutting edges (i.e. circular/square/triangular base frustums generated by laser ablation), emulating grits of these engineered abrasive tools, on the material removal mechanism for workpiece materials of different mechanical properties (ductile – copper, brittle – sapphire). 2D/3D micro-profilometry, scanning electron microscopy supported by sensory signals (e.g. cutting forces) enabled to understand the relationship between the ploughing/shearing of ductile and brittle behaviour materials upon the number and orientation of the cutting edges that emulate the tested single grit shapes. It was found that for copper the increase in number of cutting edges (NoCE) of the grits results in more localised material pile-up and the reduction of plastic deformations with inherent decrease of specific cutting force; nevertheless, it became apparent that to diminish specific cutting forces, both NoCE and effective contact area between the grit and workpiece material need to be considered. For sapphire, shearing/fracturing phenomena were preponderant in the material removal mechanism when using square/triangular shaped grits while major plastic deformations were found for circular base frustum; significant reduction of specific cutting forces were noted with the increase of NoCE. This preliminary work enables the understanding on the implications of using particular grit shapes when utilising the novel edge-controlled grinding/polishing tools for machining ductile/brittle workpiece materials.